The hosts began brightly in the opening 15 minutes, but the Rams soon gained control of the game.
The best chance of the early play fell to Jake Buxton, who sent his header from Paul Coutts's cross wide from 12 yards out.
Mason Bennett was next to call Steele into action, but once again he found the goalkeeper in top form.
The teams went into half time on a level pegging, but the visitors would soon be punished for their wastefulness in front of goal.
Indecisiveness in the Derby defence allowed Chris O'Grady the opportunity to volley the hosts into the lead two minutes after the break.
The game became tight and Nigel Clough's men struggled to break down their opponents, who defended resolutely with the one-goal advantage.
Just as the hosts looked like they had secured the win, Coutts scrambled home Richard Keogh's far-post header to rescue a point for the Rams.